Oysters, crabs, lobsters, shellfish and sharks are all non-kosher, but there is a difference between oysters and the others.  Oyster shells are rock-hard and so clearly not a food that it is generally accepted that the shell itself is “kosher”; therefore, oyster shells are approved as a (very common) source of kosher calcium.  On the other hand, the shells of crabs, lobsters and shellfish, and certainly the cartilage of sharks, are soft and flavorful enough to be given the status of the fish they come from, and are therefore non-kosher. 

Glucosamine and chondroitin are commonly produced from the soft shells and cartilage of the latter group of fish listed above, and therefore the simple understanding is that glucosamine and chondroitin are not kosher.  However, there have been some prominent Poskim who have suggested halachic rationales as to why the considerable processing done to the shells and cartilage, might do away with the non-kosher status as well.  Some Poskim accept those rationales, but most are undecided or reject such claims.  However, most of those who hold that the glucosamine and chondroitin are inherently non-kosher, agree that someone suffering from arthritis may take those items in pill form because:

• It is generally accepted that non-chewable pills are considered inedible non-foods and therefore are not required to be kosher.
• A person who is incapacitated is permitted to “eat” non-kosher medicine in an “atypical manner”, and (almost) everyone agrees that swallowing a pill is not considered eating in a typical manner.  This line of reasoning would only permit the consumption of items which have a history of being effective at curing the said illness, and at this point it seems that glucosamine and chondroitin meet that standard as a cure/relief for the symptoms of arthritis.

In summary, many hold that glucosamine and chondroitin are not kosher but they may still be taken in pill form, especially by those who suffer from arthritis, but most Rabbis would not permit the inclusion of glucosamine and chondroitin powders in regular foods.  It is worth noting that there is a company that produces glucosamine from vegetable sources, and – assuming that product retains its kosher certification – there are no questions as to the kashrus of that product, but there are those who have claimed that medically it is not as effective as the same product made from fish.